Algorithm Based on the Modified Sufficient Conditions of Inertia-Controlling Method for Globally Solution of a General Quadratic Problem

In this paper, we consider a general quadratic problem (P) with linear constraints that are not necessarily linear independent. To resolve this problem, we use a new algorithm based on the Inertia-Controlling method while replacing the condition of Lagrange multiplier vector μ by resolution of linear system obtained thanks to the Kuruch-Kuhn -Tuker matrix (KKT-matrix) in order to determine the minimize direction of (P) and so calculate the steep length in general case: indefinite, concave and convex cases. Moreover, the results presented here mark the end of the approximate methods to quadratic programming as well as the linear complementarity methods of the problems to be studied.